Here is what we currently have:
The nice thing is that they come completely out. When bad weather comes, we can remove them and replace with solid hatch boards (the best solution for bad weather I think). For a scre, we cut out screen replacement like you can get at Walmart for $5/roll to fit the hatch size. Most of the other boats that have done this like us also line the edges with sunbrella and sew in weights at the end to hold it down. It is a very cheap, easy solution.
Dad's boat (seen below), has solid teak doors with plexi glass i nthere like yours. It has a really nice knob entry with locking key mechanism. His too are removeable by pulling up. I like his bettter than ours as they are more sturdy - and I really like the knob/locking mechanism. However, as mentioned above, that would be a large set of doors for most Catalinas.
Just some thoughts, Jim.